It's a bit confusing because you're writing it. To say it, then use "three kilograms of meat". To write it, "kg" doesn't receive an s, and "three" uses the numeral: "3kg of meat". In proper, formal writing you write it out fully: "three kilograms of meat".

Agree with Peachey, let me say it my way ... My mother tongue is not English but I have studied a little bit of Physics, to tell you that: kg, m (meter) , V (Volt), W (Watt) are not abbreviations, but are meant to be symbols for the unit of measure they represent, this is not my opinion, but a definition of several decades ago; so the correct way is kg, and the plural form is in the number. Of course in commerce or in the shops we can't ask to be precise as Physicists or Biologists. If the unit comes from the name of a person (Volt, Ampere, Watt) then the symbol has the capital letter.

Three kilograms (kgs) of meat